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Re: If x > 1, what is the value of x? [#permalink]

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02 Jun 2011, 18:03

melguy wrote:

If x > 1, what is the value of x?

i) There are x unique factors of x. ii) The sum of x and any prime number larger than x is odd.

i) is understood

ii) The sum of x and any prime number larger than x is odd.

i.e if x > 1 then x has to be atleast 2 (the only prime number that is also even)

E + or - O = ODD

So only 2 will fulfill this criteria. If we take any prime number greater than 2 then O + or - O = Even.

So the answer should be each statement alone is sufficient.

Please clarify.

St2: x is not necessarily prime. x is definitely even. 4+7=11(odd); x=4, Prime Number greater than x(4) is 7; 7+4=odd 6+7=13(odd); x=6, Prime Number greater than x(6) is 7; 6+7=odd Not Sufficient.
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Re: If x > 1, what is the value of x? [#permalink]

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02 Jun 2011, 18:06

St2: x is not necessarily prime. x is definitely even. 4+7=11(odd); x=4, Prime Number greater than x(4) is 7; 7+4=odd 6+7=13(odd); x=6, Prime Number greater than x(6) is 7; 6+7=odd Not Sufficient.[/quote]

duh! Thanks for pointing out the mistake! I am just too tired and burnt out exam in 24 days

Re: If x > 1, what is the value of x? [#permalink]

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19 Jun 2016, 01:40

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(1) There are x unique factors of x --> x to have x distinct positive factors it must be divisible by EVERY integer from 1 to x, inclusive but x can not be divisible by x-1 unless x=2, for example 3 is not divisible by 2, 4 is not divisible by 3, etc, but 2 is divisible by 1 (other value of x which has x distinct positive factors (1) is excluded by the stem as x>1). So this statement implies that x=2. Sufficient.

(2) The sum of x and any prime number larger than x is odd --> x+prime=odd, now as x itself is more than 1 then prime more than x cannot be 2 thus it's odd and we have x+odd prime=odd --> x=even, so x could be ANY even number. Not sufficient.

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